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On a Conjecture of Erdős on Locally Sparse Steiner Triple Systems
A famous theorem of Kirkman says that there exists a Steiner triple system of order n if and only if n ≡ 1,3 mod 6. In 1973, Erdős conjectured that...
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Separation by Jensen and affine stochastic processes
Characterizations of pairs of stochastic processes that can be separated by Jensen and by affine stochastic processes are presented. As a...
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Moderate deviations for Euler-Maruyama approximation of Hull-White stochastic volatility model
We consider the Euler-Maruyama discretization of stochastic volatility model d S t = σ t S t d W t , d σ t = ω σ t d Z t , t ∈ [0, T ], which has been widely used in...
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On Hermite–Hadamard inequality for \({\varvec{h}}\)-convex stochastic processes
In this paper, we investigate the Hermite–Hadamard type inequality for the class of some h -convex stochastic processes, which is an extension of the...
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Comonotonic stochastic processes and generalized mean-square stochastic integral with applications
The concept of monotonic stochastic processes was introduced by Skowroński [Aequationes mathematicae 44 (
1992 ) 249–258]. In this paper, we introduce... -
Valuation of correlation options under a stochastic interest rate model with regime switching
We consider the valuation of a correlation option, a two-factor analog of a European call option, under a Hull-White interest rate model with regime...
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On fractional stochastic inequalities related to Hermite–Hadamard and Jensen types for convex stochastic processes
Stochastic convexity and its applications are very important in mathematics and probability (Aequationes Mathematicae 20:184–197,
1980 ). There are... -
Testing long memory based on a discretely observed process
In this paper we consider the problem of testing long memory for a continuous time process based on high frequency data. We provide two test...
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Refinements of mean-square stochastic integral inequalities on convex stochastic processes
Recently, in the class of convex stochastic processes, Kotrys (Aequat Math 83:143–151,
2012 ; Aequat Math 86:91–98,2013 ) proposed upper and lower... -
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Quasiconvex stochastic processes and a separation theorem
Quasiconvex stochastic processes are introduced. A characterization of pairs of stochastic processes that can be separated by a quasiconvex...
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Small deviations of iterated processes in the space of trajectories
We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under...
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Central limit theorems for power variation of Gaussian integral processes with jumps
This paper presents limit theorems for realized power variation of processes of the form X t = ∫
0 t φ s dG s + ξ t as the sampling frequency within...