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- W2083731191 abstract "Let $X{ x(t,w),{bf P}} $ be a stochastic process in n-dimensi onalEuclidean space $R_n $ having continuous trajectories, which satisfy the stochastic equation: $x^i (t,omega ) = x^i (0,omega ) + int_0^t {phi _j^i (s,omega )} + int_0^t {Psi ^i (s,omega )ds} ,quad 0 leqq t leqq 1.$Here $p = p(domega )$ is a measure in the space $Omega $ of elementary events, $int_0^t {Phi _j^i dxi ^j } $ is considered to be the stochastic integral of K. Ito with respect to the Wiener process $xi $. The process is called a Wiener process if it satisfies conditions (1.1) and (1.2) of this paper. Process X is called an K. Ito process (with respect to the Wiener process $xi $) corresponding to the diffusion matrix $phi (t,omega ) = ||phi _j^i (t,omega )||$ and to the translation vector $Psi (t,omega ) = { Psi ^i (t,omega )} $.It is proved with certain restrictions imposed on the vector $varphi (t,omega ) = { varphi ^i (t,omega )} $ that the process $tilde X = { x(t,omega ),tilde {bf P}..." @default.
- W2083731191 created "2016-06-24" @default.
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- W2083731191 date "1960-01-01" @default.
- W2083731191 modified "2023-10-17" @default.
- W2083731191 title "On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of Measures" @default.
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- W2083731191 doi "https://doi.org/10.1137/1105027" @default.
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