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4. For an Itô process {y}2o that is expressed by y = yo+foodBs+fo Hads, define the Stratonovich (stochastic) integral as 1 [3,0 dB, - [w.dB,+ [ods. σ,ds. Then, for X = Xo+ Soys o dB. + fods, prove the following, S ["p' (X₂)y, odB₁ + [*'(X₂)¸ds. (X) = (Xo) + (1)

4. For an Itô process {y}2o that is expressed by y = yo+foodBs+fo Hads, define the Stratonovich (stochastic) integral as 1 [3,0 dB, - [w.dB,+ [ods. σ,ds. Then, for X = Xo+ Soys o dB. + fods, prove the following, S ["p' (X₂)y, odB₁ + [*'(X₂)¸ds. (X) = (Xo) + (1)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. For an Itô process {y}2o that is expressed by y = yo+fo.dB, + sds, define the Stratonovich (stochastic) integral as [v₁ dB. = [x.dB. + [.dr. y, ° := σ,ds. 2 Then, for X = Xo+ Soys o dB₂+ fods, prove the following, Y(X₁) = 4(Xo) + f * Y'( '(X₂)y, odB, + [*'(X.)μ‚ds. (1)
Transcribed Image Text:4. For an Itô process {y}2o that is expressed by y = yo+fo.dB, + sds, define the Stratonovich (stochastic) integral as [v₁ dB. = [x.dB. + [.dr. y, ° := σ,ds. 2 Then, for X = Xo+ Soys o dB₂+ fods, prove the following, Y(X₁) = 4(Xo) + f * Y'( '(X₂)y, odB, + [*'(X.)μ‚ds. (1)
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