SKU: 46115775673

Inform Intro Stoch Cal (2nd Ed)

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Description

Inform Intro Stoch Cal (2nd Ed)Most branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop. Stochastic Calculus is not an easy to grasp

Most branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop. Stochastic Calculus is not an easy to grasp theory, and in general, requires acquaintance with the probability, analysis and measure theory.

 

The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author's goal was to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.

 

The second edition contains several new features that improved the first edition both qualitatively and quantitatively. First, two more chapters have been added, Chapter 12 and Chapter 13, dealing with applications of stochastic processes in Electrochemistry and global optimization methods.

 

This edition contains also a final chapter material containing fully solved review problems and provides solutions, or at least valuable hints, to all proposed problems. The present edition contains a total of about 250 exercises.

 

This edition has also improved presentation from the first edition in several chapters, including new material.

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SKU: 46115775673

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Carrie Ann Moore
West Palm Beach, US
★★★★★ 3
Cute but Not Durable
Color: 2PK Green Leaping Phrog
⭐️⭐️⭐️⭐️ Cute but Not Durable Super cute toy—my dogs loved it right away! Unfortunately, they chewed the head off within a few hours. I ordered a second one because they were so into it, but the same thing happened again. I won’t be ordering a third, but they still play with their two headless frogs. So while it’s not the most durable, it definitely kept them entertained!
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Reviewed in the United States on June 9, 2025
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Verified Purchase
Amazon Customer
Whiting, US
★★★★★ 5
Great toy
Color: Black/Orange
This brand really makes durable toys. They outlast every other toy my dogs have. One dog loves to get the squeaker out of any toy, but he doesn’t rip this one apart. Obviously it won’t last forever, but no toy does! Some other brands of toys only make it a day or two, while these last months to years.
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Reviewed in the United States on May 10, 2026
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Verified Purchase
C Harper
Lowell, US
★★★★★ 5
Super durable!
Color: 2PK Green Leaping Phrog
Yellow lab approved bc they are fun to chew. Mom approved because they last forever!
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Reviewed in the United States on January 7, 2026
A
Verified Purchase
Arele
Houston, US
★★★★★ 5
Great toy for two big German Shepherds
Color: Brown
We only buy Tuffy dog toys now because we have one German Shepherd, and we often watch our daughter's GSD too, and the two dogs tear anything else apart in minutes. Tuffy toys are BY FAR superior to any other dog toy we have tried. That being said, some Tuffy toys seem to last longer than others with the two dogs, and this one has been pretty good! We've had it for a few weeks now, and it's just now starting to show some white (stuffing) where their teeth have pierced the top of the toy. That's pretty good, considering they play tug of war with it and can tear into toys pretty hard. If it were just our one dog, I think it would last a lot longer because it's the tug of war between the two of them that does them in faster. Even so, when they do manage to tear the fabric in vulnerable places, I just pull the stuffing out from that area, and they continue to play with it, sometimes for months! This one is better than some other Tuffy toys too because it has lots of areas where there is already more fabric and reinforced seams than stuffing, like all the legs on the side, the tail, and even the pincers. So far, they haven't been able to tear into those at all. Just a bit on the top of the head, and so far, no stuffing coming out yet. This one is a big win for us! When they finally do do it in, I will turn around and buy another Scorch the Scorpion right away!
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Reviewed in the United States on May 5, 2014
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Deholle
San Leandro, US
★★★★★ 4
Tuffy Desert Phrog vs Lola
Color: Green Leaping Phrog, Color: Green Leaping Phrog
Just a little background about my dog. Lola is a 5 year old corgi-terrier mix with jaws of steal. Lesser stuffed toys have met death in under 5 minutes. Tennis balls last less than a day. Rope toys that do not have frayed ends might possibly last a week (frayed ends never stand a chance). The only toys that she has not managed to destroy are her Kong, a Kong bone, and a racquet ball. I figured I would document the life span of Phrog (Tuffy Scale: 9) before making my final judgement on it’s durability. Day 1 - Phrog Arrives! Lola was very excited about the arrival of Phrog and immediately went into destruction mode. Phrog did sustain a little damage before we were able to bribe her to drop Phrog and get her understand that he was more fun to play fetch with than to mutilate. The white you see in the picture is not stuffing, but the second layer of defense for the toy. The fact that my living room is not full of stuffing and I didn’t have to pry a squeaker out of my dog’s mouth, I’d say Phrog wins the Day 1 challenge. Day 9 - Phrog has sustained a little more damage, but not anything life threatening. His side wound is a little bit larger and one of his eyes is half ripped off. For safety reasons, I am going to finish removing the damaged eye and some loose thread from various places. Other than that, Phrog is still holding up and holds top toy spot. I have also found him very useful for dealing with anxiety; the squeaker can often distract her from her stressors and Phrog takes the abuse of her frustrations. Day 16 - Phrog is starting to show signs of mortal wounds. Lola has made it through the thicker layer around his arm and I can see the stuffing. It is only a matter of time before gets all the way through. Day 60 - Phrog still lives!!! I have done some surgery on Phrog to reinforce the fabric around his arms, but Franken-Phrog is still the favorite of all of the toys. She will even get brave enough to rescue Phrog from the evil vacuum when he is kidnapped and tortured. I am thinking about purchasing Phrog II for the inevitable day when Phrog goes off to the pet toyland in the sky, but for now, there is only one Phrog for Lola.
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Reviewed in the United States on July 6, 2018

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