Nonparametric estimation of linear multiplier for stochastic differential equations driven by multiplicative stochastic volatility
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915041824997376 |
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| author | Rao, B. L. S Prakasa |
| author_facet | Rao, B. L. S Prakasa |
| contents | We study the problem of nonparametric estimation of the linear multiplier function $θ(t)$ for processes satisfying stochastic differential equations of the type $$dX_t= θ(t)X_t dt+ ε\; σ_1(t,X_t)σ_2(t,Y_t)dW_t, X_0=x_0, 0 \leq t \leq T$$ where $\{W_t, t\geq 0\}$ is a standard Brownian motion, $\{Y_t, t\geq 0\}$ is a process adapted to the filtration generated by the Brownian motion. We study the problem of estimation of the unknown function $θ(.)$ as $ε\rightarrow 0$ based on the observation of the process $\{X_t,0\leq t \leq T\}.$ |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_00005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonparametric estimation of linear multiplier for stochastic differential equations driven by multiplicative stochastic volatility Rao, B. L. S Prakasa Statistics Theory Probability 62G05 We study the problem of nonparametric estimation of the linear multiplier function $θ(t)$ for processes satisfying stochastic differential equations of the type $$dX_t= θ(t)X_t dt+ ε\; σ_1(t,X_t)σ_2(t,Y_t)dW_t, X_0=x_0, 0 \leq t \leq T$$ where $\{W_t, t\geq 0\}$ is a standard Brownian motion, $\{Y_t, t\geq 0\}$ is a process adapted to the filtration generated by the Brownian motion. We study the problem of estimation of the unknown function $θ(.)$ as $ε\rightarrow 0$ based on the observation of the process $\{X_t,0\leq t \leq T\}.$ |
| title | Nonparametric estimation of linear multiplier for stochastic differential equations driven by multiplicative stochastic volatility |
| topic | Statistics Theory Probability 62G05 |
| url | https://arxiv.org/abs/2412.00005 |