Long-range dependent completely correlated mixed fractional Brownian motion

Shokrollahi, Foad; Sottinen, Tommi; Viitasaari, Lauri

doi:10.48550/arxiv.2104.04992

Cited by 3 publications

(8 citation statements)

References 13 publications

(19 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, we will derive the desired persistence result for a more general class of sums of selfsimilar centred Gaussian processes with different self-similarity indices, covering not only the mixed FBM M H,α , but also e.g. the case of completely correlated mixed FBM (ccmFBM) introduced in [20]. Note that the latter process neither is self-similar nor has stationary increments.…”

Section: P Sup T∈[0t]mentioning

confidence: 99%

See 1 more Smart Citation

Persistence probabilities of mixed FBM and other mixed processes

Аурзада

Kilian

Sönmez

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We consider the sum of two self-similar centred Gaussian processes with different self-similarity indices. Under the assumption of non-negative correlations and some further minor conditions, we show that the asymptotic behaviour of the persistence probability of the sum is the same as for the process with the greater self-similarity index. In particular, this covers the mixed fractional Brownian motion introduced in Cheridito (2001) and shows that the corresponding persistence probability decays asymptotically polynomially with persistence exponent 1-max(1/2,H), where H is the Hurst parameter of the underlying fractional Brownian motion.

show abstract

Section: P Sup T∈[0t]mentioning

confidence: 99%

“…As mentioned in the introduction, theorem 1 also covers the case of ccmFBM. Under this term, it was introduced recently in [20], while the process itself had already been studied as the driving process of an SDE in [37, section 3.2.3]. The definition is as follows.…”

Section: Mixed Fbm and Further Corollariesmentioning

confidence: 99%

Persistence probabilities of mixed FBM and other mixed processes

Аурзада

Kilian

Sönmez

2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…As mentioned in the introduction, Theorem 1 also covers the case of completely correlated mixed FBM. Under this term, it was introduced recently in [16], while the process itself had already been studied as the driving process of an SDE in [28, Section 3.2.3]. The definition is as follows.…”

Section: Mixed Fbm and Further Corollariesmentioning

confidence: 99%

“…In fact, we will derive the desired persistence result for a more general class of sums of self-similar centred Gaussian processes with different selfsimilarity indices, covering not only the mixed FBM M H,α , but also e.g. the case of completely correlated mixed FBM introduced in [16]. Note that the latter process neither is self-similar nor has stationary increments.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Persistence probabilities of mixed FBM and other mixed processes

Aurzada,

Kilian,

Sönmez

2022

Preprint

View full text Add to dashboard Cite

We consider the sum of two self-similar centred Gaussian processes with different self-similarity indices. Under non-negativity assumptions of covariance functions and some further minor conditions, we show that the asymptotic behaviour of the persistence probability of the sum is the same as for the single process with the greater selfsimilarity index.In particular, this covers the mixed fractional Brownian motion introduced in [13] and shows that the corresponding persistence probability decays asymptotically polynomially with persistence exponent 1 − max(1/2, H), where H is the Hurst parameter of the underlying fractional Brownian motion.

show abstract