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Problem 2. Feynman-Kac application We consider the stochastic process (X+) t20 given by X₁ = et, where (W+) is a Brownian motion. Let (W)20 and (B) to be two independent Brownian motions. We modify the system in Problem 2 to become 1 ——½X₁ dt − Y₁ dW₁ + a X₁ dBt, - - dXt = dYt = - Y₁ dt +X+dW₁+aY₁ dBt, with Xo = 1, Yo = 0 and a Є R. (a) Determine the stochastic differential equation satisfied by the processes (Rt) and (et). (b) Solve the differential equations provided in (a) for Rt. (c) Determine lim E[R] as a function of a. 0047

Problem 2. Feynman-Kac application We consider the stochastic process (X+) t20 given by X₁ = et, where (W+) is a Brownian motion. Let (W)20 and (B) to be two independent Brownian motions. We modify the system in Problem 2 to become 1 ——½X₁ dt − Y₁ dW₁ + a X₁ dBt, - - dXt = dYt = - Y₁ dt +X+dW₁+aY₁ dBt, with Xo = 1, Yo = 0 and a Є R. (a) Determine the stochastic differential equation satisfied by the processes (Rt) and (et). (b) Solve the differential equations provided in (a) for Rt. (c) Determine lim E[R] as a function of a. 0047

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 1EQ: In Exercises 1-12, find the solution of the differential equation that satisfies the given boundary...
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please solve problem 4. Thank you

Problem 2. Feynman-Kac application We consider the stochastic process (X+) t20 given by X₁ = et, where (W+) is a Brownian motion.
Transcribed Image Text:Problem 2. Feynman-Kac application We consider the stochastic process (X+) t20 given by X₁ = et, where (W+) is a Brownian motion.
Let (W)20 and (B) to be two independent Brownian motions. We modify the system in Problem 2 to become 1 ——½X₁ dt − Y₁ dW₁ + a X₁ dBt, - - dXt = dYt = - Y₁ dt +X+dW₁+aY₁ dBt, with Xo = 1, Yo = 0 and a Є R. (a) Determine the stochastic differential equation satisfied by the processes (Rt) and (et). (b) Solve the differential equations provided in (a) for Rt. (c) Determine lim E[R] as a function of a. 0047
Transcribed Image Text:Let (W)20 and (B) to be two independent Brownian motions. We modify the system in Problem 2 to become 1 ——½X₁ dt − Y₁ dW₁ + a X₁ dBt, - - dXt = dYt = - Y₁ dt +X+dW₁+aY₁ dBt, with Xo = 1, Yo = 0 and a Є R. (a) Determine the stochastic differential equation satisfied by the processes (Rt) and (et). (b) Solve the differential equations provided in (a) for Rt. (c) Determine lim E[R] as a function of a. 0047
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