We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the addition of additive noise in the vertical direction leads to a unique invariant probability measure to which the system converges at a uniform, exponential rate. These facts are established primarily through the construction of a Lyapunov function which we generate as the solution to a sequence of Poisson equations. Unlike a number of other works, however, our Lyapunov function is constructed in a systematic way, and we present a meta-algorithm we hope will be applicable to other problems. We conclude by proving positivity properties of the transition density by using Malliavin calculus via some unusually explicit calculations.
Introduction
The relationship between masturbation activities and their effect on partnered sex is understudied.
Aim
The aim of this study was to assess the alignment of activities between masturbation and partnered sex, and to determine whether different levels of alignment affect orgasmic parameters during partnered sex.
Methods
2,215 women completed an online survey about activities during masturbation and reasons for orgasmic difficulty during masturbation, and these were compared with activities and reasons for orgasmic difficulty during partnered sex.
Main Outcome Measure
Degree of alignment between masturbation activities and partnered sex activities was used to predict sexual arousal difficulty, orgasmic probability, orgasmic pleasure, orgasmic latency, and orgasmic difficulty during partnered sex.
Results
Women showed only moderate alignment regarding masturbation and partnered sex activities, as well as reasons for masturbation orgasmic difficulty and reasons for partnered sex orgasmic difficulty. However, those that showed greater alignment of activities showed better orgasmic response during partnered sex and were more likely to prefer partnered sex over masturbation.
Clinical Implications
Women tend to use less conventional techniques for arousal during masturbation compared with partnered sex. Increasing alignment between masturbation and partnered sexual activities may lead to better arousal and orgasmic response, and lower orgasmic difficulty.
Strength & Limitations
The study was well-powered and drew from a multinational population, providing perspective on a long-standing unanswered question. Major limitations were the younger age and self-selection of the sample.
Conclusion
Women that align masturbation stimulation activities with partnered sex activities are more likely to experience orgasm and enhanced orgasmic pleasure, with sexual relationship satisfaction playing an important role in this process.
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