Weak solutions for stochastic differential equations with additive fractional noise
We give a new approach to prove the existence of a weak solution of \[dx_t = f(t,x_t)dt + g(t)dB^H_t\] where $B^H_t$ is a fractional Brownian motion with values in a separable Hilbert space for suitable functions $f$ and $g$. Our idea is to use the implicit function theorem and the scaling property...
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| creator | Catuogno, Pedro J Ledesma, Diego S |
| description | We give a new approach to prove the existence of a weak solution of \[dx_t =
f(t,x_t)dt + g(t)dB^H_t\] where $B^H_t$ is a fractional Brownian motion with
values in a separable Hilbert space for suitable functions $f$ and $g$. Our
idea is to use the implicit function theorem and the scaling property of the
fractional Brownian motion in order to obtain a weak solution for this
equation. |
| doi_str_mv | 10.48550/arxiv.2206.07159 |
| format | Article |
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f(t,x_t)dt + g(t)dB^H_t\] where $B^H_t$ is a fractional Brownian motion with
values in a separable Hilbert space for suitable functions $f$ and $g$. Our
idea is to use the implicit function theorem and the scaling property of the
fractional Brownian motion in order to obtain a weak solution for this
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f(t,x_t)dt + g(t)dB^H_t\] where $B^H_t$ is a fractional Brownian motion with
values in a separable Hilbert space for suitable functions $f$ and $g$. Our
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f(t,x_t)dt + g(t)dB^H_t\] where $B^H_t$ is a fractional Brownian motion with
values in a separable Hilbert space for suitable functions $f$ and $g$. Our
idea is to use the implicit function theorem and the scaling property of the
fractional Brownian motion in order to obtain a weak solution for this
equation.</abstract><doi>10.48550/arxiv.2206.07159</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Probability |
| title | Weak solutions for stochastic differential equations with additive fractional noise |
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